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Clicking data, which exists in abundance and contains objective userpreference information, is widely used to produce personalized recommendationsin web-based applications. Current popular recommendation algorithms, typicallybased on matrix factorizations, often have high accuracy and achieve goodclickthrough rates. However, diversity of the recommended items, which cangreatly enhance user experiences, is often overlooked. Moreover, mostalgorithms do not produce interpretable uncertainty quantifications of therecommendations. In this work, we propose the Bayesian Mallows for ClickingData (BMCD) method, which augments clicking data into compatible full rankingvectors by enforcing all the clicked items to be top-ranked. User preferencesare learned using a Mallows ranking model. Bayesian inference leads tointerpretable uncertainties of each individual recommendation, and we alsopropose a method to make personalized recommendations based on suchuncertainties. With a simulation study and a real life data example, wedemonstrate that compared to state-of-the-art matrix factorization, BMCD makespersonalized recommendations with similar accuracy, while achieving much higherlevel of diversity, and producing interpretable and actionable uncertaintyestimation.

Diverse personalized recommendations with uncertainty from implicit preference data with the Bayesian Mallows Model